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Latest blogosphere posts tagged “set theory”
I spent the last week trying to get clear on the logical interconnections between a number of results about probabilities that are relevant to formal epistemology and that use a version of the Axiom of Choice in proof, such as: For every non-empty set Ω, there is an ordered field K and a K -valued probability ...2 weeks ago
Suppose you have assigned coherent (i.e., finitely additive) probabilities to a collection of options, but then you come upon a refinement of this collection of options, including more fine-grained ones. For instance, previously you had assigned probabilities to propositions about which individuals in a population ...2 weeks ago
The Hahn-Banach Theorem (HB) cannot be proved without some version of the Axiom of Choice. (Technically, its stronger than ZF but weaker than BPI.) A cool fact about HB is that it is sufficient for proving the existence of nonmeasurable sets and even for proving the Banach-Tarski paradox . In the 1970s, ...3 weeks ago
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